How to show activity (which cannot be converted to fragment) using BottomNavigationBar?

I have problem with showing my activity. I don't know how to implement methods from NoteActivity to HomeFragment. HomeFragment is carried out by BottomNavigationBar without executing a NoteActivity.

NoteActivity-

    public class NoteActivity extends AppCompatActivity {
    private FirebaseFirestore db = FirebaseFirestore.getInstance();
    private CollectionReference notebookRef = db.collection("Notebook");

    private NoteAdapter adapter;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.fragment_home);

        setUpRecyclerView();
    }

    public void setUpRecyclerView() {
        Query query = notebookRef.orderBy("title", Query.Direction.DESCENDING);

        FirestoreRecyclerOptions<Note> options = new FirestoreRecyclerOptions.Builder<Note>()
                .setQuery(query, Note.class)
                .build();

        adapter = new NoteAdapter(options);

        RecyclerView recyclerView = findViewById(R.id.recycler_view);
        recyclerView.setHasFixedSize(true);
        recyclerView.setLayoutManager(new LinearLayoutManager(this));
        recyclerView.setAdapter(adapter);
    }

    @Override
    protected void onStart() {
        super.onStart();
        adapter.startListening();
    }

    @Override
    protected void onStop() {
        super.onStop();
        adapter.stopListening();
    }
}

Simple HomeFragment which should have content of NoteActivity-

 public class HomeFragment extends Fragment {
    @Nullable
    public View onCreateView(LayoutInflater inflater, @Nullable ViewGroup container, @Nullable Bundle savedInstanceState) {
        return inflater.inflate(R.layout.fragment_home, container, false); 
    }
}

BottomNavigationBar which is executing HomeFragment and 2 more activities -

public class BottomNavigationBar extends AppCompatActivity {

    @Override
    public void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_bottom);
        BottomNavigationView bottomNav = findViewById(R.id.bottom_navigation);
        bottomNav.setOnNavigationItemSelectedListener(navListener);
        bottomNav.setSelectedItemId(R.id.nav_home);
    }

    private BottomNavigationView.OnNavigationItemSelectedListener navListener =
            new BottomNavigationView.OnNavigationItemSelectedListener() {
                @Override
                public boolean onNavigationItemSelected(@NonNull MenuItem item) {
                    Fragment selectedFragment = null;

                    switch (item.getItemId()) {
                        case R.id.nav_home:
                            selectedFragment = new HomeFragment();
                            break;
                        case R.id.nav_game:
                            selectedFragment = new GameFragment();
                            break;
                        case R.id.nav_user:
                            selectedFragment = new UserFragment();
                            break;
                    }

                    getSupportFragmentManager()
                            .beginTransaction()
                            .replace(R.id.fragment_container,
                                    selectedFragment)
                            .commit();

                    return true;
                }
            };
}

Please help, thanks.